The invention relates to the field of radio navigation and, more specifically, the invention relates to the methods for determining the current values of the orbital position of the artificial satellite of the Earth operating in a satellite radio navigation system (SRNS) by the ephemeredes, and can be used for performing the radio navigation measurements in the equipment of the users of the SRNS signals.
It is well known, that the navigational receivers in the equipment of the users of the SRNS GPS and/or GLONASS signals, determine their coordinates and speed using the quasi-range and quasi-velocity measurements relative to the current position (coordinates) of satellites on orbit (cf. Network Satellite Radio Navigation Systems, V. S. Sebshaevich, P. P. Dmitriev, N. V. Ivantsevich et al., Moscow, Radio i Svyaz publishers, 1993, pages 110-114, FIG. 7.3) [1]. The current values of the coordinates of the satellites at the moments of measurements are calculated in the receiver. The calculation is based on the ephemeris data transmitted by each SRNS satellite. Since the ephemeredes of the satellite are the coordinate and the velocity and acceleration component defined by the Sun and Moon attraction and are transmitted only during defined periods of time, all current (intermediate) coordinates of the satellite on its orbit are determined by means of prediction including extrapolation (see [1] pages 20-21, 29-31, 165-166, 171-173).
The known methods of determining the current orbital position (coordinates) of the SRNS satellite are based on the prediction (extrapolation) of the orbital motion stemming from the a priori known coordinates of the satellite on the orbit at a given instant of time and taking into account the known disturbing factors. The commonly known forms of representation of the orbital motion are temporal polynomials in the rectangular coordinates; harmonic approximations in the rectangular coordinates; temporal polynomials in elements; harmonic approximations in the elements (cf. [1], page 172).
The known methods of determination if the current coordinates of the SRNS satellite based on the prediction (extrapolation) of the orbital motion are characterized by a high cost of computational procedures (complex and costly processors are used) and a low speed of response.
A computationally simple method of calculations is based on the use of the orbit of the polynomial approximations in coordinates (cf. [1], page 172).
Known in the art is a more accurate but low-speed method based on the representation of the orbital motion as a harmonic approximation in the elements (cf. [1]) page 172-173). Also known in the art is an example of successive calculations of the orbital motion based on such a method, as applied to the SRNS GPS satellite (see, or example, GPS Navigation Message, A. J. Van Dierendonck, S. S. Russell, E. R. Kopitzke et al., Navigation (USA), 1978. Vol.25, #2, p. 146-165) [2]. A specific feature of the method [2] is that the same algorithm of evaluations is used at any instant, and since the calculations are made in a full scope at each instant of time, the speed of response of this method is also low.
A similar disadvantage may be found n the method recommended by the document xe2x80x9cICD GPS-200xe2x80x9d (cf. ICD Navstar GPS Space Segment/Navigation User Interface) [3] as a standard method of determining the current coordinates of the SRNS GSP satellite. In practice, the time of calculation of one point on the orbit is effected, on the average, in 1.850 ms.
As a prior art, a relevant method is described in the xe2x80x9cInterface Control Documentxe2x80x9d for the GLONASS system (cf Global Navigational Satellite Systemxe2x80x94GLONASS, Interface Control Document KNITS VKS Research Institute, Russia 1995 [4] recommended as a standard for determining the current coordinates of the satellite by the ephemeredes). In various embodiments of practical realization, the prior art method can use the Runge-Kutta technique of the fourth order for integration of the differential equations of motion of the satellite on orbit, extrapolation and construction of a predicted path. The calculation time in this method depends on the value of the extrapolation interval. For realization of the prior art method there can also be used a more cost-effective computational technique based on the six-order Taylor polynomial ensuring the accuracy required in the differential method of navigational determinations. The time of calculation by the Taylor polynomial (processor TMS320C203, language xe2x80x9cCxe2x80x9d, the data with a fixed point only) is equal to 0.675 ms for one satellite.
The realization of the prior art method is rather complex in the computational aspect, especially in the case of using a simple inexpensive processor (for example, without hardware support of the operations with a floating point), where the calculations might require an unacceptably long time. This is associated with the fact that the standard and rather complex algorithm of calculations is applied for an instant of time, i.e. for the calculation of all current points of orbital motion of the satellite.
The claimed invention solves an engineering problem of reduction of the computing and time expenses when determining the path of the SRNS satellite, i.e. makes it possible to use relatively simple and inexpensive processors while reducing the time of calculations.
This task is attained by using a combined (two-step) process of determining the path of a satellite, when the standard algorithm is used for calculation of only definite nodal points of the pathxe2x80x94once in a time interval, while the calculation of the intermediate point of the path within this interval is effected by means of a simplified procedure, i.e. using simple polynomial formulas whose coefficients are calculated at the first step of application of the standard computational algorithm.
The essence of the invention is described as follows. In the method of determining the coordinates of the SRNS satellite on the orbit by the ephemeredes, where a priori known ephemeredes at an initial time instant are used for determining the extrapolated position of the satellite on orbit at a series of arbitrary points, a standard computational algorithm is used for determining the coordinates of the satellite only at some nodal points of the orbit spaced from each other by a selected time interval. In addition, the satellite velocity is determined at the nodal points. Meanwhile, at the intermediate points between the nodal points, the satellite position is determined using a simplified computational algorithm based on polynomial formulas, the coefficients for which are calculated based on the coordinates and velocity of the satellite at the nodal points.
In a method according to an embodiment of the invention, the coordinates and velocity of the SRNS GLONASS satellite at the nodal points of the orbit are determined using the standard computational procedure and the six-order Taylor polynomial, while the satellite coordinates at the intermediate orbital points are determined using the Taylor polynomial of the second or third order.